Reduce to lowest terms: $ \dfrac{5}{3} \div \dfrac{5}{6} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{5}{6}$ is $ \dfrac{6}{5}$ Therefore: $ \dfrac{5}{3} \div \dfrac{5}{6} = \dfrac{5}{3} \times \dfrac{6}{5} $ $ \phantom{ \dfrac{5}{3} \times \dfrac{6}{5}} = \dfrac{5 \times 6}{3 \times 5} $ $ \phantom{ \dfrac{5}{3} \times \dfrac{6}{5}} = \dfrac{30}{15} $ The numerator and denominator have a common divisor of $15$, so we can simplify: $ \dfrac{30}{15} = \dfrac{30 \div 15}{15 \div 15} = 2 $